Fig. 1. Large singular function device via forward design method to ultra-compact multi-function device via inverse design method^{[19,35,42-43]}

Fig. 2. Genetic algorithm. (a) Design process; (b) optimized reflector^[27]; (c) optimized polarization rotator^[28]

Fig. 3. Particle swarm optimization algorithm. (a) Design process; (b) optimized power beam splitter ^[29]; (c) optimized polarization beam splitter^[30]

Fig. 4. Direct binary search algorithm. (a) Design process; (b) optimized polarization beam splitter^[31]; (c) optimized mode (de) multiplexer^[32]

Fig. 5. Topological optimization algorithm. (a) Principle of topological optimization^[44]; (b) design process of the dense gradient topological optimization method; (c) optimized polarization beam splitter^[34]; (d) optimized mode (de) multiplexer^[35]

Fig. 6. Target priority algorithm. (a) Optimized mode size converter^[37]; (b) optimized optical diode^[38]

Fig. 7. Level set method^[40]. (a) Optimized 1×3 power splitter; (b) optimized three-channel wavelength (de) multiplexer

Fig. 8. Inverse-designed SOI grating couplers^[48-53]

Fig. 9. Parameters related to inverse-designed 3 dB power splitter^[44,54-60]

Fig. 10. Devices obtained based on inverse design method. (a) Optical cloak^[65]; (b) optical router^[66]; (c) optical diode^[67]

Fig. 11. Devices obtained based on inverse design method. (a) Filter^[100]; (b) reflector^[27]

Fig. 12. Parameters related to inverse-designed wavelength (de) multiplexer^{[19,23,36,101-102]}